Finite Group Databasebeta

← C139×#33837 #48028433

Subgroups — C139×#33837 #48028433

Order 35584.

680 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C139C211yesmaximal, characteristic, complemented
2C2×#508×C139C211yesmaximal, characteristic, complemented
3#3287×C139C211yesmaximal, characteristic, complemented
4#3285×C139C211yesmaximal, characteristic, complemented
5#2250×C139C211yesmaximal, characteristic, complemented
6#2218×C139C211yesmaximal, characteristic, complemented
7#2217×C139C211yesmaximal, characteristic, complemented
8#2211×C139C211yesmaximal, characteristic, complemented
9#2207×C139C211yesmaximal, characteristic, complemented
10#2189×C139C211yesmaximal, characteristic, complemented
11#2186×C139C211yesmaximal, characteristic, complemented
12#2186×C139C211yesmaximal, characteristic, complemented
13#2185×C139C211yesmaximal, characteristic, complemented
14#2176×C139C211yesmaximal, characteristic, complemented
15#2168×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139C2211yescharacteristic
17C2×#135×C139C2211yescharacteristic
18C2×#135×C139C2211yescharacteristic
19C22×Q16×C139C2211yescharacteristic
20#550×C139—21no—
21#548×C139—21no—
22#510×C139—24no—
23#508×C139—24no—
24C2×Q32×C139C2211yescharacteristic
25C2×Q32×C139C2211yescharacteristic
26C2×SD32×C139C2211yescharacteristic
27C2×SD32×C139C2211yescharacteristic
28C2×SD32×C139C2211yescharacteristic
29C2×SD32×C139C2211yescharacteristic
30C2×SD32×C139C2211yescharacteristic
31C2×D16×C139C2211yescharacteristic
32C2×D16×C139C2211yescharacteristic
33C2×M32×C139C2211yescharacteristic
34C22×C16×C139C2211yescharacteristic
35#495×C139C2211yescharacteristic
36#493×C139C2211yescharacteristic
37#467×C139C2211yescharacteristic
38#466×C139C2211yescharacteristic
39#466×C139C2211yescharacteristic
40#466×C139C2211yescharacteristic
41#464×C139—21no—
42#460×C139—21no—
43#452×C139—21no—
44#449×C139—21no—
45#449×C139—21no—
46#448×C139—21no—
47C4×Q16×C139C2211yescharacteristic
48C4×Q16×C139C2211yescharacteristic
49C8×D4×C139C2211yescharacteristic
50#367×C139C2211yescharacteristic
51C4⋊C16×C139C2211yescharacteristic
52#358×C139C2211yescharacteristic
53#358×C139C2211yescharacteristic
54#358×C139C2211yescharacteristic
55#357×C139C2211yescharacteristic
56#357×C139C2211yescharacteristic
57#357×C139C2211yescharacteristic
58C22⋊C16×C139C2211yescharacteristic
59C22⋊C16×C139C2211yescharacteristic
60#346×C139C2211yescharacteristic
61C2×#41×C139—21no—
62C2×#41×C139—21no—
63C2×#41×C139—21no—
64C22×Q8×C139—21no—
65#135×C139—22no—
66#135×C139—22no—
67#135×C139—22no—
68#135×C139—41no—
69#135×C139—41no—
70#135×C139—41no—
71C2×Q16×C139—22no—
72C2×Q16×C139—21no—
73C2×Q16×C139—41no—
74C2×Q16×C139C2311yescharacteristic
75C2×Q16×C139C2311yescharacteristic
76C2×Q16×C139C2311yescharacteristic
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139—21no—
80C2×SD16×C139—21no—
81C2×D8×C139—21no—
82C2×D8×C139C2311yescharacteristic
83C2×D8×C139C2311yescharacteristic
84C2×D8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87#127×C139—21no—
88#127×C139—41no—
89#124×C139—21no—
90#124×C139—41no—
91C22⋊Q8×C139—21no—
92C22⋊Q8×C139—41no—
93#121×C139—21no—
94#121×C139—21no—
95#121×C139—21no—
96#121×C139—41no—
97#121×C139—41no—
98#121×C139—41no—
99C4×Q8×C139—21no—
100C4×Q8×C139—21no—
101C4×D4×C139—41no—
102C4×D4×C139—41no—
103C4×D4×C139D411yescharacteristic
104Q32×C139—22no—
105Q32×C139D414yescomplemented
106SD32×C139—22no—
107SD32×C139—22no—
108SD32×C139—22no—
109SD32×C139—22no—
110SD32×C139—41no—
111D16×C139—22no—
112D16×C139—41no—
113M32×C139—22no—
114C2×C16×C139—22no—
115C2×C16×C139C2311yescharacteristic
116C2×C16×C139C2311yescharacteristic
117C2×C16×C139C2311yescharacteristic
118C2×C16×C139C2311yescharacteristic
119#107×C139C2311yescharacteristic
120#107×C139C2311yescharacteristic
121C4⋊C8×C139D411yescharacteristic
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#102×C139—21no—
126#102×C139—21no—
127#102×C139—21no—
128C22⋊C8×C139D411yescharacteristic
129C22⋊C8×C139D411yescharacteristic
130C4×C8×C139C2311yescharacteristic
131#41×C139—42no—
132#41×C139—42no—
133#41×C139—42no—
134#41×C139—81no—
135#41×C139—81no—
136#41×C139—81no—
137C2×Q8×C139—21no—
138C2×Q8×C139—21no—
139C2×Q8×C139—21no—
140C2×Q8×C139—42no—
141C2×Q8×C139—41no—
142C2×Q8×C139—81no—
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139—41no—
147C2×D4×C139—41no—
148C2×D4×C139—41no—
149C2×D4×C139—41no—
150C2×D4×C139—41no—
151C2×D4×C139—41no—
152C2×D4×C139—41no—
153C2×D4×C139—41no—
154C2×D4×C139D811yescharacteristic
155C22×C4×C139—41no—
156C22×C4×C139—41no—
157C22×C4×C139—41no—
158C22×C4×C139—41no—
159C22×C4×C139C2×D411yescharacteristic
160C22×C4×C139C2×D411yescharacteristic
161Q16×C139—21no—
162Q16×C139—21no—
163Q16×C139—21no—
164Q16×C139—21no—
165Q16×C139—42no—
166Q16×C139C2×D412yes—
167Q16×C139C2×D412yes—
168SD16×C139—42no—
169SD16×C139—42no—
170SD16×C139—42no—
171SD16×C139—81no—
172D8×C139—21no—
173D8×C139—21no—
174D8×C139—21no—
175D8×C139—21no—
176D8×C139—21no—
177D8×C139—21no—
178D8×C139—81no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139C2×D411yescharacteristic
184C2×C8×C139C2×D411yescharacteristic
185C2×C8×C139C2×D411yescharacteristic
186C2×C8×C139C2411yescharacteristic
187C4⋊C4×C139—21no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139—41no—
191C4⋊C4×C139—41no—
192C4⋊C4×C139D811yescharacteristic
193C22⋊C4×C139—41no—
194C22⋊C4×C139—41no—
195C22⋊C4×C139—41no—
196C22⋊C4×C139—41no—
197C22⋊C4×C139—41no—
198C22⋊C4×C139—41no—
199C22⋊C4×C139D811yescharacteristic
200C22⋊C4×C139D811yescharacteristic
201C42×C139—41no—
202C42×C139—41no—
203C42×C139C2×D411yescharacteristic
204C16×C139—21no—
205C16×C139—21no—
206C16×C139—21no—
207C16×C139C2×D412yes—
208C23×C139—41no—
209C23×C139—41no—
210C23×C139—41no—
211C23×C139C2×D811yescharacteristic
212C23×C139C2×D811yescharacteristic
213Q8×C139—22no—
214Q8×C139—22no—
215Q8×C139—41no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—82no—
220D4×C139—41no—
221D4×C139—41no—
222D4×C139—41no—
223D4×C139—41no—
224D4×C139—41no—
225D4×C139—41no—
226D4×C139—41no—
227D4×C139—82no—
228D4×C139—82no—
229D4×C139—82no—
230D4×C139—82no—
231D4×C139—82no—
232D4×C139—161no—
233D4×C139—161no—
234D4×C139—161no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—82no—
245C2×C4×C139—82no—
246C2×C4×C139—82no—
247C2×C4×C139—82no—
248C2×C4×C139C2×D811yescharacteristic
249C2×C4×C139C2×D811yescharacteristic
250C2×C4×C139C2×D811yescharacteristic
251C2×C4×C139C2×D811yescharacteristic
252C2×C4×C139C22×D411yescharacteristic
253C8×C139—21no—
254C8×C139—21no—
255C8×C139—21no—
256C8×C139C22×D411yescharacteristic
257C8×C139H(5,𝔽2)11yescharacteristic
258C22×C139—21no—
259C22×C139—21no—
260C22×C139—21no—
261C22×C139—21no—
262C22×C139—21no—
263C22×C139—21no—
264C22×C139—81no—
265C22×C139—81no—
266C22×C139—81no—
267C22×C139—81no—
268C22×C139—81no—
269C22×C139—81no—
270C22×C139—81no—
271C22×C139—81no—
272C22×C139—81no—
273C22×C139C22×D811yescharacteristic
274C4×C139—21no—
275C4×C139—21no—
276C4×C139—21no—
277C4×C139—21no—
278C4×C139—42no—
279C4×C139—42no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139—81no—
283C4×C139D4211yescharacteristic
284C4×C139#57611yescharacteristic
285C2×C139—41no—
286C2×C139—41no—
287C2×C139—161no—
288C2×C139—161no—
289C2×C139—161no—
290C2×C139D4×D811yescharacteristic
291C2×C139#341411yescharacteristic
292C2×C139#341611yescharacteristic
293#33837C13911yesmaximal, characteristic, direct product factor, Sylow
294C139#3383711yescharacteristic, direct product factor, Sylow
295C2×#510C2×C13911yescharacteristic, complemented
296C2×#508C2×C13911yescharacteristic, complemented
297#3287C2×C13911yescharacteristic, complemented
298#3285C2×C13911yescharacteristic, complemented
299#2250C2×C13911yescharacteristic, complemented
300#2218C2×C13911yescharacteristic, complemented
301#2217C2×C13911yescharacteristic, complemented
302#2211C2×C13911yescharacteristic, complemented
303#2207C2×C13911yescharacteristic, complemented
304#2189C2×C13911yescharacteristic, complemented
305#2186C2×C13911yescharacteristic, complemented
306#2186C2×C13911yescharacteristic, complemented
307#2185C2×C13911yescharacteristic, complemented
308#2176C2×C13911yescharacteristic, complemented
309#2168C2×C13911yescharacteristic, complemented
310C2×#135C22×C13911yescharacteristic
311C2×#135C22×C13911yescharacteristic
312C2×#135C22×C13911yescharacteristic
313C22×Q16C22×C13911yescharacteristic
314#550—21no—
315#548—21no—
316#510—24no—
317#508—24no—
318C2×Q32C22×C13911yescharacteristic
319C2×Q32C22×C13911yescharacteristic
320C2×SD32C22×C13911yescharacteristic
321C2×SD32C22×C13911yescharacteristic
322C2×SD32C22×C13911yescharacteristic
323C2×SD32C22×C13911yescharacteristic
324C2×SD32C22×C13911yescharacteristic
325C2×D16C22×C13911yescharacteristic
326C2×D16C22×C13911yescharacteristic
327C2×M32C22×C13911yescharacteristic
328C22×C16C22×C13911yescharacteristic
329#495C22×C13911yescharacteristic
330#493C22×C13911yescharacteristic
331#467C22×C13911yescharacteristic
332#466C22×C13911yescharacteristic
333#466C22×C13911yescharacteristic
334#466C22×C13911yescharacteristic
335#464—21no—
336#460—21no—
337#452—21no—
338#449—21no—
339#449—21no—
340#448—21no—
341C4×Q16C22×C13911yescharacteristic
342C4×Q16C22×C13911yescharacteristic
343C8×D4C22×C13911yescharacteristic
344#367C22×C13911yescharacteristic
345C4⋊C16C22×C13911yescharacteristic
346#358C22×C13911yescharacteristic
347#358C22×C13911yescharacteristic
348#358C22×C13911yescharacteristic
349#357C22×C13911yescharacteristic
350#357C22×C13911yescharacteristic
351#357C22×C13911yescharacteristic
352C22⋊C16C22×C13911yescharacteristic
353C22⋊C16C22×C13911yescharacteristic
354#346C22×C13911yescharacteristic
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C22×Q8—21no—
359#135—22no—
360#135—22no—
361#135—22no—
362#135—41no—
363#135—41no—
364#135—41no—
365C2×Q16—22no—
366C2×Q16—21no—
367C2×Q16—41no—
368C2×Q16C23×C13911yescharacteristic
369C2×Q16C23×C13911yescharacteristic
370C2×Q16C23×C13911yescharacteristic
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×D8—21no—
376C2×D8C23×C13911yescharacteristic
377C2×D8C23×C13911yescharacteristic
378C2×D8C23×C13911yescharacteristic
379C22×C8C23×C13911yescharacteristic
380C22×C8C23×C13911yescharacteristic
381#127—21no—
382#127—41no—
383#124—21no—
384#124—41no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—41no—
391#121—41no—
392#121—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×D4—41no—
396C4×D4—41no—
397C4×D4D4×C13911yescharacteristic
398Q32—22no—
399Q32D4×C13914yescomplemented
400SD32—22no—
401SD32—22no—
402SD32—22no—
403SD32—22no—
404SD32—41no—
405D16—22no—
406D16—41no—
407M32—22no—
408C2×C16—22no—
409C2×C16C23×C13911yescharacteristic
410C2×C16C23×C13911yescharacteristic
411C2×C16C23×C13911yescharacteristic
412C2×C16C23×C13911yescharacteristic
413#107C23×C13911yescharacteristic
414#107C23×C13911yescharacteristic
415C4⋊C8D4×C13911yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8D4×C13911yescharacteristic
423C22⋊C8D4×C13911yescharacteristic
424C4×C8C23×C13911yescharacteristic
425#41—42no—
426#41—42no—
427#41—42no—
428#41—81no—
429#41—81no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8—41no—
436C2×Q8—81no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4D8×C13911yescharacteristic
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C13911yescharacteristic
454C22×C4C2×D4×C13911yescharacteristic
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—21no—
459Q16—42no—
460Q16C2×D4×C13912yes—
461Q16C2×D4×C13912yes—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465SD16—81no—
466D8—21no—
467D8—21no—
468D8—21no—
469D8—21no—
470D8—21no—
471D8—21no—
472D8—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8C2×D4×C13911yescharacteristic
478C2×C8C2×D4×C13911yescharacteristic
479C2×C8C2×D4×C13911yescharacteristic
480C2×C8C24×C13911yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4D8×C13911yescharacteristic
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4D8×C13911yescharacteristic
494C22⋊C4D8×C13911yescharacteristic
495C42—41no—
496C42—41no—
497C42C2×D4×C13911yescharacteristic
498C16—21no—
499C16—21no—
500C16—21no—
501C16C2×D4×C13912yes—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C2×D8×C13911yescharacteristic
506C23C2×D8×C13911yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—82no—
524D4—82no—
525D4—82no—
526D4—161no—
527D4—161no—
528D4—161no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4C2×D8×C13911yescharacteristic
543C2×C4C2×D8×C13911yescharacteristic
544C2×C4C2×D8×C13911yescharacteristic
545C2×C4C2×D8×C13911yescharacteristic
546C2×C4C22×D4×C13911yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8C22×D4×C13911yescharacteristic
551C8H(5,𝔽2)×C13911yescharacteristic
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C22×D8×C13911yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4D42×C13911yescharacteristic
578C4#576×C13911yescharacteristic
579C2—41no—
580C2—41no—
581C2—161no—
582C2—161no—
583C2—161no—
584C2D4×D8×C13911yescharacteristic
585C2#3414×C13911yescharacteristic
586C2#3416×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×D4×C139 ◁ C8×D4×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#510×C139C2semidirect
2. C2×#508×C139C2semidirect
3. #3287×C139C2semidirect
4. #3285×C139C2semidirect
5. #2250×C139C2semidirect
6. #2218×C139C2semidirect
7. #2217×C139C2semidirect
8. #2211×C139C2semidirect
9. #2207×C139C2semidirect
10. #2189×C139C2semidirect
11. #2186×C139C2semidirect
12. #2186×C139C2semidirect
13. #2185×C139C2semidirect
14. #2176×C139C2semidirect
15. #2168×C139C2semidirect
105. Q32×C139D4semidirect
293. #33837C139direct (N × H)
294. C139#33837direct (N × H)
295. C2×#510C2×C139semidirect
296. C2×#508C2×C139semidirect
297. #3287C2×C139semidirect
298. #3285C2×C139semidirect
299. #2250C2×C139semidirect
300. #2218C2×C139semidirect
301. #2217C2×C139semidirect
302. #2211C2×C139semidirect
303. #2207C2×C139semidirect
304. #2189C2×C139semidirect
305. #2186C2×C139semidirect
306. #2186C2×C139semidirect
307. #2185C2×C139semidirect
308. #2176C2×C139semidirect
309. #2168C2×C139semidirect
399. Q32D4×C139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#510×C1392
C2×#508×C1392
#3287×C1392
#3285×C1392
#2250×C1392
#2218×C1392
#2217×C1392
#2211×C1392
#2207×C1392
#2189×C1392
#2186×C1392
#2185×C1392
#2176×C1392
#2168×C1392
#33837139